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# Mass excess

The mass excess of a nuclide is the difference between its mass number and its actual mass. [1] It is not the same as binding energy, although the concepts are related.[2]It is a useful quantity when deciding whether a radioactive decay will occur and, if it does, how much energy will be released. Radioactive decay processes will only occur if the mass excess of the products is less than the mass excess of the parent nuclide.

The difference between the mass number and actual mass arises from the mass-energy equivalence E=mc². When two nucleons come together, the potential energy between them due to the strong nuclear force is converted to mass. Qualitatively, if a nuclide has a high mass excess, this indicates that the nucleus is tightly bound.

## Example

Consider the nuclear fission of 236U into 92Kr 141Ba and three neutrons.

236U → 92Kr + 141Ba + 3 n

The mass number of 236U is 236 u (atomic mass units), but the actual mass is 236.045563 u, so the mass excess is − 0.045563 u. Calculated in the same manner, the mass excess for 92Kr, 141Ba, and a neutron are − 0.073843 u, − 0.085588 u and 0.0086648 u, respectively. The mass excess of the reactant is − 0.045563 u, and the mass excess of the products is − 0.073843 + ( − 0.085588) + 3 * (0.0086648) = − 0.1334366 The difference between reactants and products is − 0.1334366 − ( − 0.045563) = − 0.0878736 u, which shows that the mass excess of the products is less than that of the reactants, and so the decay can occur.

The resulting difference in mass excess can be converted into energy using 1 u = 931.502 MeV/c², yielding 81.8544 MeV.

## References

1. ^ [1]
2. ^ [2]
• Kenneth S. Krane 1987. Introductory Nuclear Physics John Wiley & Sons ISBN 0-471-80553-X
• Paul A Tipler, Ralph A. Llewellyn 2004. Modern Physics WH Freeman and Co. ISBN 0-716-74345-0